5x-7=4 ------ 7 где полосочки это дробная черта

The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep

Alchen [17]

Ooh, fun

geometric sequences can be represented as
$a_n=a(r)^{n-1}$
so the first 3 terms are
$a_1=a$
$a_2=a(r)$
$a_2=a(r)^2$

the sum is -7/10
$\frac{-7}{10}=a+ar+ar^2$
and their product is -1/125
$\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3$

from the 2nd equation we can take the cube root of both sides to get
$\frac{-1}{5}=ar$
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
$\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r$
subsituting -1/5 for ar
$\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r$
which simplifies to
$\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}$
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for $ax^2+bx+c=0$
$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$
so
for 2r²-5r+2=0
a=2
b=-5
c=2

$r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}$
$r=\frac{5 \pm \sqrt{25-16}}{4}$
$r=\frac{5 \pm \sqrt{9}}{4}$
$r=\frac{5 \pm 3}{4}$
so
$r=\frac{5+3}{4}=\frac{8}{4}=2$ or $r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}$

use them to solve for the value of a
$\frac{-1}{5}=ar$
$\frac{-1}{5r}=a$
try for r=2 and 1/2
$a=\frac{-1}{10}$ or $a=\frac{-2}{5}$

test each
for a=-1/10 and r=2
a+ar+ar²= $\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}$
it works

for a=-2/5 and r=1/2
a+ar+ar²= $\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}$
it works

both have the same terms but one is simplified

the 3 numbers are $\frac{-2}{5}$ , $\frac{-1}{5}$ , and $\frac{-1}{10}$

6 0

2 years ago

Share 747 pound in the ratio 2:7 betwen tom and ben

Yuliya22 [10]

2p + 7p = 747
9p = 747 divded by 9 = 83
2 * 83 = 166 7 * 83 = 581

Hope it helps

7 0

2 years ago

Please help me make 3 sentences with the above proverbs

nasty-shy [4]

I don't know if this is what you mean, sorry!!

Answer:

1: "You can't lie because Honesty is the best policy!"

2: "Wake up! You know that The early bird catches the worm!"

3: "It will be okay, Every cloud has a silver lining."

Hope this helps!!

4 0

2 years ago

Pleas answer quickly

alexandr1967 [171]

Step-by-step explanation:

I don't understand, why there is this segment about the 0 degrees Kelvin.

any material, water or the glass the water is in, or the air, or the floor or the wall : the higher the temperature (the scale does not matter, as long both temperatures use the same), the more energy it contains (the faster the particles in that substance are moving/vibrating).

therefore a glass of water with 80 degrees will have much more energy than one with 20 degrees.

the same way an aluminum can (the actual name of that material is aluminium, but Americans seemingly cannot pronounce that) with 30 degrees has more energy than one with 20 degrees.

3 0

2 years ago

I Have To Show My Work Help I'm Stuck

Katena32 [7]

The answer is 64.5

1/4 of 86, divide 86 by 4 is 21.5. Then u multiply that by 3 since this is only 1/4. You would get a result of 64.5.

Eric is 64.5 inches tall :)

8 0

2 years ago

Read 2 more answers